The article deals with the development of the theory of stochastic cooperative games and also possible future directions of practical applications of this class of games are considered. The principal feature of the proposed approach to stochastic cooperative games is that it is based on the definition of the imputation as a vector, which provides the conditions of individual and group rationality with a certain (given) the probability alpha. Unlike previous approaches, that consider imputation in stochastic cooperative game as "fixed" proportions, our view is to consider total utility of the coalition as a random variable, distributed among its participants. This approach introduces the concept of alpha-core games and consideres a number of problems that can be formulated with respect to the properties of this object.